Free-form reinforced concrete, prestressed concrete, and composite components: Calculation of cross-section values

A resource-efficient use of concrete as a construction material can be achieved by adapting the individual shape of a component under consideration to the stresses that occur and by arranging composite construction materials (e.g., reinforcing steel, prestressing steel, or structural steel) in suitable areas of the component. Due to the advancing digitalization in the construction industry, for example in the context of Building Information Modeling, computer-aided 3D modeling methods are increasingly being used in the planning of structures. These allow engineers to design components in free form. In reinforced concrete, prestressed concrete, and composite construction, the design of such components is currently still associated with great effort. In the context of the development of a practical method for the calculation of free-form concrete components, this paper presents a CAD-integrated method for the calculation of cross-section values. Cross-section values are required as an essential calculation basis when real, three-dimensional structural components are treated using simplified calculation theories, such as the beam theory. In this paper, the mathematical and numerical fundamentals of a method for the calculation of cross-section values of free-form concrete, reinforced concrete, prestressed concrete, and compound components are presented. The calculation method is based on flat geometric regions described by Non-uniform Rational B-Spline tensor product surfaces, which can be extracted from solid models, for example.